PAL: Program-aided Language Models

Chain-of-thought prompting made language models much better at word problems by having them write out intermediate steps. It left a gap: the model can decompose a problem correctly and still get 93 + 39 wrong, and the errors multiply with larger numbers or longer chains. Luyu Gao, Aman Madaan, Shuyan Zhou, Graham Neubig and colleagues at Carnegie Mellon asked why the model should do the arithmetic at all.

PAL, program-aided language models, keeps the model's role to understanding the problem and writing the steps, but writes those steps as Python. The few-shot prompt shows example questions answered with short programs: meaningful variable names, comments in plain language, and a final answer variable. Given a new question, the model writes a similar program, a Python interpreter runs it, and the result is the answer. The model never computes anything itself.

Across 13 tasks, eight math word-problem sets, three symbolic-reasoning tasks from BIG-Bench Hard and two algorithmic tasks, PAL with the Codex code model beat chain-of-thought prompting with the same model, and often beat much larger models. The most telling result is GSM-HARD, the authors' version of GSM8K with one number in each problem replaced by an integer of up to seven digits. Chain of thought fell from 65.6% to 23.1%; PAL went from 72.0% to 61.2%.

Customer workflows are full of arithmetic: invoice totals, prorated refunds, inventory counts, date windows, unit conversions. A model that reasons in prose will occasionally get the arithmetic wrong, confidently and invisibly. PAL is the pattern that removes that class of error.

Never let the model do the math in text. Have it produce an expression, a small program or a structured calculation that code executes. The paper's large-number test shows how fast in-text arithmetic degrades.

The remaining errors are reading errors. A program that subtracts returned items instead of adding them runs perfectly and gives the wrong answer. The interpreter guarantees the arithmetic, not the interpretation. Validate inputs and add sanity checks to generated programs.

Readable code is reviewable. Variable names and comments make each step inspectable, by a person or by an automated check. That is an audit trail chain of thought does not give you.

It is the seed of code actions. PAL is one program per question with no feedback. CodeAct and later agents extend the same idea to multi-step tasks with tools and error messages.

Sandbox it. Running model-written code needs the same containment as any code action, even when it only does arithmetic.